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-BARSIC- [3]
3 years ago
13

A nonzero polynomial with rational coefficients has all of the numbers [1 sqrt{2}, ; 2 sqrt{3}, ;3 sqrt{4},; dots, ;1000 sqrt{10

01}]as roots. What is the smallest possible degree of such a polynomial?
Mathematics
1 answer:
Colt1911 [192]3 years ago
8 0

Answer:

Its degree can be at least 1970

Step-by-step explanation:

for each root of the form √q, where q is not a square, we have a root -√q. Therefore, we need to find, among the numbers below to 1000, how many sqaures there are.

Since √1000 = 31.6, we have a total of 30 squares:

2², 3², 4², ...., 30², 31²

Each square gives one root and the non squares (there are 1000-30 = 970 of them) gives 2 roots (one for them and one for the opposite). Hence the smallest degree a rational polynomial can have is

970*2 + 30 = 1970

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The sea turtle habitat at the zoo is made by connecting two large aquariums. The first aquarium is 6\text { m}6 m6, space, m lon
iren [92.7K]

First aquarium dimensions:

Length = 6 m.

Width = 4 m and

Height = 2 meter.

Second aquarium dimensions:

Length = 8 m.

Width = 9 m and

Height = 3 meter.

We know formula for volume of a cuboidal box = Length*Width*Height.

Plugging values of length, width and height of first aquarium in formula of volume. We get

V1 = 6*4*2 = 48 m^3.

Plugging values of length, width and height of second aquarium in formula of volume. We get

V2 = 8*9*3 = 216 m^3.

In order to find the total cubic meters of space do the sea turtles have in their habitat, we need to add both volumes.

Therefore, Total voulme of both aquarium = V1 +V2 = 48+216 = 264 m^3.

Therefore, total 264 m^3 cubic meters of space the sea turtles have in their habitat.

8 0
3 years ago
Can you help me fill in the blanks?
Pepsi [2]


10 pints = 5 quarts

4   pints = 2 quarts

6   pints = 3 quarts

2   pints = 1 quart

The Bold numbers are the ones you need to fill in.

Hope that helps :D

8 0
3 years ago
Ben left a 20% tip on his bill at a restaurant. The bill was $40
tigry1 [53]

Answer:

Tip: $8

Total:$48

Step-by-step explanation:

Multiply 40 by 20% to find out how much money he gave for tip.

Add the amount of tip, 8, to $40 find out the total amount of money he spent.

3 0
3 years ago
How do you put 300,000+10,000+6,000+20+9
dsp73

Answer:

three hundred thousand plus ten thousand plus six thousand plus twenty plus nine

Step-by-step explanation:

300,000 → three hundred thousand

10,000 → ten thousand

6,000 → six thousand

20 → twenty

9 → nine

+ → plus

Now put everything together.

Best of Luck!

3 0
3 years ago
Can someone show me how to factor this? 5k-35
kaheart [24]
Sure.
Can you find a number that goes into both terms, 5k and 35 ?
How about 5 ?

(5k - 35) = 5 times (k - 7) .
6 0
3 years ago
Read 2 more answers
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